\xiti

解下列方程：

\begin{xiaotis}

\xiaoti{$2\sin 2x + 1 = 0$。}

\xiaoti{$\sin\left( \dfrac{x}{2} + \dfrac{\pi}{6} = \dfrac{\sqrt{3}}{2} \right)$。}

\xiaoti{$2\cos\left( \dfrac{x}{3} + 45^\circ \right) = 1$。}

\xiaoti{$\tan 2x - \sqrt{3} = 0$。}

\xiaoti{$\dfrac{1}{2} \cot 2(x + 25^\circ) - 2 = 0$。}

\xiaoti{$2\cos^2 x - 3\cos x + 1 = 0$。}

\xiaoti{$\sin^2 2x = \sin 2x$。}

\xiaoti{$3\sin x - 2\cos^2 x = 0$。}

\xiaoti{$2\sin^2 x = 1$。}

\xiaoti{$\sin^2 x - 7\sin x \cos x + 6\cos^2 x = 0$。}

\xiaoti{$\sin x \cos x = \dfrac{1}{4}$。}

\xiaoti{$3\sin^2 x - \sin 2x - \cos^2 x = 0$。}

\xiaoti{$\sin 3x = \sin x$。}

\xiaoti{$\sin 2x = \cos 3x$。}

\xiaoti{$\sin \left( 2x + \dfrac{\pi}{3} \right) + \sin \left( x - \dfrac{\pi}{6} \right) = 0$。}

\xiaoti{$\sin \left( x + \dfrac{\pi}{6} \right) + \cos \left( x + \dfrac{\pi}{6} \right) = 0$。}

\xiaoti{$5\cos 2x + 2\sin 2x = 0$。}

\xiaoti{$\cos^2 2x - 3\sin^2 2x = 0$。}

\xiaoti{$\sin\dfrac{x}{2} - \cos\dfrac{x}{2} = 1$。}

\xiaoti{$4\sin x + 3\cos x = 3$。}

\end{xiaotis}
